\[\large du=3t^2 dt \qquad \rightarrow \qquad \color{orangered}{\frac{1}{3}du=t^2dt}\]I would have changed the 1/3 in this step, but the way you did it works fine also! :) It looks like you replaced dt with du, you didn't replace the t^2 hmm

\[\large \int\limits t^2(t^3-3)^{10}dt \qquad \rightarrow \qquad \frac{1}{3}\int\limits 3t^2(t^3-3)^{10}dt\]I understand what you were doing here, you put a 1/3 and 3 in to fix things up. But you also threw in a t^2! woops! :)